Strong no-go theorem for Gaussian quantum bit commitment

Loïck Magnin (1) , Frédéric Magniez (2, 1) , Anthony Leverrier (3, 4) , Nicolas J. Cerf (5)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LRI - Laboratoire de Recherche en Informatique
3 Laboratoire Charles Fabry de l'Institut d'Optique / Optique quantique
4 LTCI - Laboratoire Traitement et Communication de l'Information
5 ULB - Université libre de Bruxelles

Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.

Domaines: Physique Quantique [quant-ph]

Loïck Magnin, Frédéric Magniez, Anthony Leverrier, Nicolas J. Cerf. Strong no-go theorem for Gaussian quantum bit commitment. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2010, 81, pp.010302(R). ⟨10.1103/PhysRevA.81.010302⟩. ⟨hal-00639629⟩